lecture18 - 1 ECE 303 – Fall 2005 – Farhan Rana –...

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Unformatted text preview: 1 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Lecture 18 Reflection and Transmission of Waves at Interfaces In this lecture you will learn: • What happens when waves strike an interface between two different media • Reflection and transmission of waves at interfaces • Application of E-field and H-field boundary conditions ECE 303 – Fall 2005 – Farhan Rana – Cornell University Waves at Interfaces Consider a plane wave given by: ( ) z k j i i e E x r E − = ˆ r r incident upon an interface between medium “ i ” and medium “ t ” z =0 z z k k i ˆ = r E i H i • When the incident wave strikes the interface, it generates a transmitted wave and a reflected wave • We need to find the amplitudes of these reflected and transmitted waves o i µ ε o t µ ε x 2 ECE 303 – Fall 2005 – Farhan Rana – Cornell University Waves at Interfaces – E-Fields z =0 z z k k i ˆ = r E i H i Incident, transmitted, and reflected waves z k k i ˆ − = r E r H r z k k t ˆ = r E t H t For z < 0 the total E-field is: ( ) z k j r z k j i z i i e E x e E x r E + − < + = ˆ ˆ r r i o i k ε µ ω = For z > 0 the total E-field is: ( ) z k j t z t e E x r E − > = ˆ r r t o t k ε µ ω = In the above equations, E r and E t are the unknowns that we need to find in terms of the incident field amplitude E i o i µ ε o t µ ε x ? ? ECE 303 – Fall 2005 – Farhan Rana – Cornell University Waves at Interfaces – Boundary Conditions z =0 z z k k i ˆ = r E i H i z k k i ˆ − = r E r H r z k k t ˆ = r E t H t For z < 0: ( ) z k j r z k j i z i i e E x e E x r E + − < + = ˆ ˆ r r For z > 0: ( ) z k j t z t e E x r E − > = ˆ r r Use boundary conditions: (1) At z = 0 the E-field parallel to the interface must be continuous This gives: t r i E E E = + o i µ ε o t µ ε x 3 ECE 303 – Fall 2005 – Farhan Rana – Cornell University z =0 z z k k i ˆ = r E i H i z k k i ˆ − = r E r H r z k k t ˆ = r E t H t (2) At z = 0 the H-field parallel to the interface must be continuous (no surface currents) Waves at Interfaces – H-fields For z < 0: ( ) z k j i r z k j i i z i i e E y e E y r H + − < − =...
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This note was uploaded on 02/02/2008 for the course ECE 3030 taught by Professor Rana during the Fall '06 term at Cornell University (Engineering School).

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lecture18 - 1 ECE 303 – Fall 2005 – Farhan Rana –...

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